Home > Inequalities, Olympiad > IMC 2013 Problem 4

IMC 2013 Problem 4


Problem 4. Let {n \geq 3} and let {x_1,..,x_n} be nonnegative real numbers. Define {A=\sum\limits_{i=1}^n x_i, B = \sum\limits_{i=1}^n x_i^2} and {C= \sum\limits_{i=1}^n x_i^3}. Prove that

\displaystyle (n+1)A^2B +(n-2)B^2 \geq A^4+(2n-2)AC.

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Categories: Inequalities, Olympiad Tags: ,
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